Conical defects in growing sheets

Abstract

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle $se$ at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if $se<=0$, the disc can fold into one of a discrete infinite number of states if $se$ is positive. We construct these states in the regime where bending dominates, determine their energies and how stress is distributed in them. For each state a critical value of $se$ is identified beyond which the cone touches itself. Before this occurs, all states are stable; the ground state has two-fold symmetry.

4 pages, 4 figures, LaTeX, RevTeX style. New version corresponds to the one published in PRL

References in corpus (2)

• Morphogenesis of growing soft tissues
• How paper folds: bending with local constraints

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